I've been discussing the issue of the missing 42nd generation with a good friend of mine, and quite frankly, we're stuck. We've searched through Kings and Chronicles and it seems like Jeconiah is in fact the grandson of Josiah and son of King Jehoakim. Matthew clearly leaves out other names and for what reason, it's hard to say if we'll ever know. But it seems to me that Matthew is leaving us a bit of a mystery with this one, intentionally omitting the generation after Jesus Christ because his offspring are yet to be determined. For our generation will not come by physical birth, but by spiritual birth (John 1:12-13) -- Jason Tibesar
Easy answer, actually. Jehoiakim and Jehoiachin are BOTH represented by Jeconiah (Matt 1:11-12)! It's the same word in Greek. And, as you notice, Matthew, like many writers of genealogies, is more concerned with the spiritual point than with strict and comprehensive accuracy. The ancestors of Jesus fall into three equally long generations. Jesus gives us a way to see history: Abraham to David, David to the Exile, Exile to Messiah. That is, he was following the canons of ancient genealogy, not trying to conform to modern conventions.
The other explanation may also have merit, though it makes an unnecessary assumption, given what we know about counting systems and genealogical conventions in the ancient world.